Solid `Ba(NO_(3))_(2)` is gradually dissolved in a `1.0xx10^(-4)M Na_(2)CO_(3)` solution. At what concentration of `Ba^(2+)` will a precipitate begin to form ? `(K_(sp) " for for " BaCO_(3)=5.1xx10^(-9))`

Options

A. `5.1xx10^(-5)M`
B. `8.1xx10^(-8)M`
C. `8.1xx10^(-7)M`
D. `4.1xx10^(-5)M`

Answer

A

Explanation

`underset(1xx10^(-4)M)(Na_(2)CO_(3)) to underset(1xx10^(-4)M)(2Na^(+))+ underset(1xx 10^(-4)M)(CO_(3)^(2-))`
`K_(sp(BaCO_(3)))=[Ba^(2+)][CO_(3)^(2-)]`
`[Ba^(2+)]=(5.1xx10^(-9))/(1xx10^(-4))=5.1xx10^(-5)M`